Archer served as a justice on the Michigan Supreme Court from 1986 to 1990. In his last year as a Michigan Supreme Court justice, he was named "most respected judge in Michigan" by Michigan Lawyers Weekly.

Archer served as mayor of Detroit from 1993 to 2001. As mayor, he worked to repair the city's relations with the Detroit suburbs and the local business community through cooperation with suburban business leaders on their redevelopment plans for the city, reducing tensions.

As mayor, Archer was never popular with loyalists of his predecessor, Coleman Young. Young favored Sharon McPhail, a former member of the Detroit City Council, and wished for her to succeed him. In the 1993 race to succeed Young, Archer (who is black) did not win a majority of the black vote. Archer was re-elected by a large margin in 1997, but was subject to a recall campaign in his second term, launched by many of his original opponents. He declined to run for re-election in 2001.[5]

Upon leaving office as Mayor of Detroit in January 2002, Archer was appointed as chairman of Detroit-based law firmDickinson Wright, and the board of directors of Compuware.[6] He is a Fellow of the Litigation Counsel of America.